It was once a place you ventured in a tin helmet, with your fingers stuffed in your ears. After the fall of Tripoli last August, rebels celebrated by firing round after round of bullets into the night sky. The debris of battle and revolution was everywhere.

There are no weapons to be seen in Martyrs' Square now. Instead the square has been turned into a children's playground with a Superman bouncy castle, a toy train, and outdoor table football. There is a market with women's clothes and shoes. Other stalls sell kalashnikovs – the plastic variety – and cups of mint tea.

Sitting in a cafe across from the square's imposing Ottoman palace, Saad Kamur explained that he had voted for Mahmoud Jibril in Libya's historic election. Jibril, a 60-year-old US-educated political scientist, appears to have won a landslide victory in the poll on Saturday, defying predictions that Islamists would sweep to power in Libya, as they have done elsewhere.

"He's moderate. And experienced," Kamur said. "I don't think the others were capable of running a government." Kamur, a Tripoli businessman, said observers who predicted that Libya would go the way of Egypt and Tunisia – now run by religious parties – had misinterpreted the national mood, and Libya's prevailing centrism.

"Libyans are open to the outside world. Many have studied abroad. They haven't seen anything positive yet from Islamist governments," he suggested. As for the election, in which he cast his first ever vote at the rather belated age of 52, he said: "Nobody imagined it would go this smoothly."

Abdul Muntasar, a purveyor of squeaky dog-toys for eight dinars each, said he liked Jibril because he was nothing like Libya's previous ruler Muammar Gaddafi, who was caught and killed last October.

"Jibril isn't a man trying to seize power," he said. Ahmed Ibrahim, a tourist visiting from provincial Al-Jufra, chipped in: "He's educated, on the side of democracy."

Indeed, Libya's new leader has a reputation as a pragmatic moderate.

He attracted votes from all points on the country's political compass: from liberals and the educated in Tripoli; from tribesmen in the desert south; and – in an arguably hopeful sign for reconciliation – from disgruntled former supporters of the previous regime.

Until last October Jibril was interim prime minister in the National Transitional Council (NTC). Speaking on Sunday night, he indicated he was willing to put together a grand coalition to rule post-Gaddafi Libya. It will include Islamist groups, as well as others in the country's new ascendancy, balancing regional, religious and tribal forces.

Jibril's biggest advantage over his defeated rivals was his high profile. During the brief election campaign he was frequently on TV. Western educated and English-speaking, Jibril had – controversially for some – worked for the Gaddafi regime as head of the national Economic Development Board.

His defection to the rebel NTC was conducted with impeccable timing at the beginning of last year's revolution.

Appointed its de facto prime minister, he was the prime mover in winning support from the west for Libya's then-opposition, earning plaudits at home.

Jibril is a member of the powerful Warfalla tribe from Bani Walid. The town was of the last to fall during the revolution and has a reputation – unfair, its elders say – as a pro-Gaddafi stronghold.

This fact may have contributed to his resignation last October, when a new cabinet was appointed under the current prime minister, Abdurrahim El Keib.

Some said Jibril's close association with the previous Gaddafi regime raised questions over his judgement. Jibril worked with Saif al-Islam – Gaddafi's son and one-time heir – over a proposed new constitution. He resigned when it became clear that Saif, who is in custody charged with war crimes, was unwilling to pursue a genuinely reformist agenda.

"He definitely has ties with the old regime. He was a Saifist," Noora Ahmed, 18, said, strolling with two friends on to Martyrs' Square from Tripoli's atmospheric medina (old town). "This doesn't make him illegitimate. But there is always a bit of underlying suspicion when someone was prepared to put up with, or work with, the Gaddafis."

Ahmed conceded that Jibril had enthused Libya's youth to vote for him in huge numbers.

Others said they felt that what post-Gaddafi Libya needed was an emphatic break from personality politics.

"Personality is our problem," Mahmoud Amer, a foreign ministry civil servant, observed. "I think Libya doesn't want one person," he added. "We've had 42 years of dictatorship. What we need now is a coalition. We need a leadership group made up of different parties."

Amer said Saturday's democratic vote was the moment the Gaddafi era was finally consigned to history's capacious dustbin. Asked why the country's Islamist parties hadn't done better, he replied: "Libyans are in the middle. The majority isn't to the right or the left. We have a dislike of extremism."

Certainly, extreme religious groups have so far gained little traction in Libya, despite sporadic attacks in parts of the east of the country on Sufi shrines and on western targets, including the British ambassador, whose convoy in Benghazi was attacked recently. In Tripoli, for example, the white stucco Italianate alleyways around Martyrs' Square are home to beauty parlours and boutiques selling flowing evening dresses and less modest shorter skirts – a nightmare for hardline Salafists.

As prime minister, Jibril will face a host of problems. He will have to assuage federalists in the east of the country who have expressed dissatisfaction – sometimes violently – at their share of seats in the new national congress. (The west of the country has been given 100 seats, the east 60 and the south 40. The allocation has been done on the basis of population, but has fuelled Benghazi's long-standing feelings of exclusion and resentment.)

There are other challenges, too: on human rights, disarming the country's powerful militias, and on kick-starting economic growth.

Amer suggested Jibril's biggest challenge was what to do with the country's enormous oil revenues, most of which vanished without trace during the Gaddafi regime.

According to those who have met him, Jibril has many presidential qualities. But he is not known for his jokes. "He does have charisma. But to be a politician and have a sense of humour – well, they don't go together," Kamur said.

• This article was amended on 11 July 2012 to clarify Jibril's position in the Gaddafi regime.